Polystyrene universal calibration curve

PMMA, on the unmodified porous glass and silica gel, and the universal calibration curves for polystyrenes and poly(methyl methacrylates) did not coincide (10,12,19). 

The most widely used molecular weight characterization method has been GPC, which separates compounds based on hydrodynamic volume. State-of-the-art GPC instruments are equipped with a concentration detector (e.g., differential refractometer, UV, and/or IR) in combination with viscosity or light scattering. A viscosity detector provides in-line solution viscosity data at each elution volume, which in combination with a concentration measurement can be converted to specific viscosity. Since the polymer concentration at each elution volume is quite dilute, the specific viscosity is considered a reasonable approximation for the dilute solution s intrinsic viscosity. The plot of log[r]]M versus elution volume (where [) ] is the intrinsic viscosity) provides a universal calibration curve from which absolute molecular weights of a variety of polymers can be obtained. Unfortunately, many reported analyses for phenolic oligomers and resins are simply based on polystyrene standards and only provide relative molecular weights instead of absolute numbers. 

Figure 3, HDC universal calibration curve (eluant ionic strength L29rriM. AM A monodisperse lattices (O) polystyrene polyvinyl chloride ( ) poly (styrene-...

Figure 19 shows the Universal Calibration Curve obtained for the coupled GPCs in terms of the hydrodynamic volume in THF (Ref Table II). The addition of the n-Heptane caused a dramatic shift downstream of the polystyrene standards. 

For many polymers K and a values can be found in the Polymer Handbook [23]. In a recent study by Vanhee et al. [30] the universal calibration has been applied using the polystyrene (PS) calibration curve to characterize rigid rod poly(p-phenylenes) (PPP). It turned out that due to its larger persistence length, PPP with a certain mass requires a much larger volume than PS for the same molecular weight. Ron et al. employed universal calibration for the characterization of erodible copolymers [58]. 

Novolac molecular weights were measured in THF at 35°C by high pressure size exclusion chromatography using a Waters Model 510 pump (flow rate=1.0 ml/min), 401 differential viscometer detector and a set of Dupont PSM 60 silanized columns. A universal calibration curve was obtained with a kit of 10 narrow molecular weight distribution, linear polystyrene standards from Toya Soda Company. Data acquisition and analysis were performed on an AT T 6312 computer using ASYST Unical 3.02 software supplied with the Viscotek instrument. 

From the primary calibration curve based on polystyrene standards and the Mark-Houwink constants for polystyrene (K,a) a universal calibration curve (Z vs. v), based on hydrodynamic volume is constructed. Z is calculated from... 

Figure 10 shows DRI and viscometer traces for the NBS 706 polystyrene standard. Based on the information from these two chromatograms in conjunction with the universal calibration curve, one can calculate the intrinsic viscosity EnJCv) and molecular weight M(v) at each retention volume as shown in... 

A universal calibration curve was developed, using the retention volume vm corresponding to the DRl detector peak maximum of eluting polystyrene calibrants. Data were fitted with the GPC-II program to an equation of the form ... 

Figure 1. Master universal calibration curve obtained with a Beckman /z-Spherogel column system in THF. The fit of narrow MWD standards, polystyrene star polymers, and a single broad MWD standard (calculated with Unical 2.71 software) are shown.

Values for system peak parameters were found using a narrow distribution polystyrene standard (PS68K) before calculating MWD data for the lignin samples from universal calibration. To check software and instrument operation, several narrow MWD polystyrene and one broad MWD polymethylmethacrylate standards were treated as unknown samples and subjected to analysis with the universal calibration curve assembled from all polymer standards files. It was found that the MWD could be estimated for the recalculated polymer standards with errors between 5 and 10% of the original value indicated by the supplier of the standard (e.g., Mw for PS11K and Mw and M for PMMA17K-6). 

A universal calibration curve (log [> ] Mw vs. elution vol.) was prepared for the gel permeation chromatograph using samples of anionically prepared polystyrene (Fig. 7). The figure includes samples of polyf4-methyl-1 -pentene). It has been found that polymers for which the relationship between log[ ] Mw and the G.P.C. elution volume is linear are generally Gaussian coils in solution. 

A universal calibration curve was established by plotting the product of the limiting viscosity numbers and molecular weight, Mw[iy], vs. the elution volume, EV, for a variety of characterized polymers. The major usefulness of the universal calibration curve was to validate individual molecular-weight values and to provide extended molecular-weight calibration at the ends of the calibration curve where fractions of narrow dispersion of the polymer being analyzed are not available. The calibration curve was monitored daily with polystyrene fractions certified by Pressure Chemicals. The relationship between the polyethylene fractions and polystyrene fractions was determined using the universal calibration curve. 

If the Mark-Houwink coefficients are not available, a universal calibration curve is established using polystyrene calibration standards and the SEC-vis-cometer combination. The basic steps involved in the MMD analysis are summarized in Fig. 11. First, the universal calibration curve of the SEC separation system has to be established by using narrow molar mass standards as indicated by the top arrow pointing to the right. Once the universal calibration curve is established, the procedure can then be reversed, by going from right to left following the bottom arrow, to obtain the molar mass calibration curve of any unknown... 

The utility of the universal calibration curve is that it allows us to calculate the molecular weight of a polydisperse polymer sample for which we do not have monodis-perse standards. First, a universal calibration curve is prepared for a given set of columns using, say, monodisperse polystyrene samples. This is plotted as log J versus elution volume (Figure 12-43) where for the rth sample (Equation 12-62) ... 

The next step is to make sure the data fits a universal calibration curve prepared using polystyrene standards (also in THF at 30°C). The plot of J M7] versus elution volume shown in Figure 12-50 shows that the fit is... 

Universal calibration curve for size exclusion chromatography. Data points are polybutadienes in tetrahydrofuran at 25 °C in crosslinked polystyrene columns. There is a reasonably linear region of the calibration curve spanning the data (solid line) but the linear region has its limits (dotted curves). 

The SEC columns were calibrated using narrow molecular weight distribution water soluble polymer standards sodium polystyrene sulfonate, NaPSS (Pressure Chemical Company, Pittsburgh, PA) and dextrans (Pharmacia Fine Chemicals, Piscataway, NJ). The universal calibration curve proposed by Grubisic et al. (13) was found not to be applicable for these polymer standards. The alternative calibration procedure of Coll and Prusinowski (J ) which incorporates excluded volume effects in the numerical value of the Flory parameter was found to be applicable for this system ( ). The calibration curve for the two-column network system described above is shown in Figure 3. The Kyyy parameter used on the abscissa of Figure 3 is a normalized elution volume parameter defined by Equation 1,... 

The SEC elution times are dependent on molecular hydrodynamic volume rather than molecular weight, M, as is the intrinsic viscosity, [ ]. Thus the idea of a universal calibration curve is proposed (53) in which log ]A/is plotted versus the elution volume. Brule (12) shows a single curve for a number of asphalts, although it still deviates from the universal curve established for polystyrene or other polymers (49). In fact, there is considerable deviation from the universal curve for aromatic and highly condensed compounds (54,87). 

Silanized silica gel has also been studied for the SEC analysis of cellulose trinitrate (37,38), using THF as the eluant. It was concluded that the elution behavior of the cellulose trinitrate sample was influenced by polyelectrolytic effects and was not based strictly upon size exclusion. The addition of 0.01 mol acetic acid per liter THF suppressed the non-size exclusion effects. Under these conditions, a universal calibration curve relating cellulose trinitrate and polystyrene could be established. 

DMAc is a new solvent for starch SEC analysis. It has not yet been used widely. Polystyrene is soluble in DMAc. This solvent may have the advantage of using polystyrene to construct the universal calibration curve. Polystyrene standards are cheaper, and their molecular weight can be as high as 21 million. 

The universal calibration curve was constructed with polystyrene having narrow MMD by using the equation... 

The Mark-Houwink constants influence the accuracy of the universal calibration curve. The discrepancy between universal calibration curves for PS and P(VC-VAc) copolymers observed by Chen and Blanchard [15] may be due to misuse of the Mark-Houwink constants for polystyrene. These authors obtained the Mark-Houwink equation for P(VC-VAc) copolymers as... 

Fig. 26. Universal calibration curve for SEC. Polystsrrene (linear) O polystyrene ( comb ) + polystyrene ( star ) A polystyrene-poly(methylmethacrylate) copolymer (heterograft) x poly(methylmethacrylate) (linear) poly(vinylchloride) V polystyrene-poly(methylmethacrylate) copolymer (graft-comb) Bpolylphenyl siloxane) A polystyrene-poly(methylmethacrylate) copolymer (statistical-linear) n polybutadiene. From Ref 31.

Figure 3.23 The universal calibration curves for polystyrene and poly(vinyl acetate) (94), The number 5 in the x-axis units means that the scale is in siphon counts of 5 cm so that the x-ordinate 30 corres 3onds to an elution volume of 150cm (R. Dietz, private communication, November 1984,) Mr is the peak GPC molecular weight, usually the unknown, Rvalues are close to the geometric mean of M and M .

Figure 3.52. Universal calibration curve of SEC. The plots of M[i ] obtained for poly(methyl methacrylate), poly(ethylene oxide), and polystyrene are on a master curve. The mobile phase was dimethylacetamide. (From Ref. 39.)...

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